Discrete Mathematics is the mathematics of distinct, countable structures. It is the essential mathematical foundation for computer science.

Key Topics

• Logic and Proofs — Propositional logic, predicates, quantifiers, and proof techniques (direct, contradiction, induction).
• Set Theory — Sets, subsets, unions, intersections, power sets, and cardinality.
• Functions — Injections, surjections, bijections, and composition.
• Combinatorics — Counting principles, permutations, combinations, and the pigeonhole principle.
• Graph Theory — Vertices, edges, paths, cycles, trees, and graph coloring.
• Number Theory — Divisibility, primes, modular arithmetic, and the Euclidean algorithm.
• Relations — Reflexive, symmetric, transitive, and equivalence relations.
• Boolean Algebra — Logic gates, circuits, and simplification.

Why It Matters

Discrete math is the math of algorithms, data structures, cryptography, networks, and databases. If you study computer science, this is your most important mathematics course alongside linear algebra.